Terminology for elements in modules

• Dec 19th 2009, 05:47 AM
crwtom
Terminology for elements in modules
I am looking for an adjective for special elements in modules.

Definition: Let $R$ be a ring and $M$ be an $R$-module.
We say that $v\in M$ is an ????? element if $v=rw$
with $w\in M$ and $r\in R$ implies that $r$ has to be a unit in $R$.

What is the commonly used term ???? for this definition?

In the lattice case $R=\mathbb Z$ and $M=\mathbb Z^N$ these are often called
primitive vectors but this terminology does not seem to be common
for general rings and modules.

Thanks ---
• Dec 19th 2009, 02:06 PM
NonCommAlg
Quote:

Originally Posted by crwtom
I am looking for an adjective for special elements in modules.

Definition: Let $R$ be a ring and $M$ be an $R$-module.
We say that $v\in M$ is an ????? element if $v=rw$
with $w\in M$ and $r\in R$ implies that $r$ has to be a unit in $R$.

What is the commonly used term ???? for this definition?

In the lattice case $R=\mathbb Z$ and $M=\mathbb Z^N$ these are often called
primitive vectors but this terminology does not seem to be common
for general rings and modules.

Thanks ---

why is the terminology important here? if you have a "math" question related to this, you can ask.